Use the image to answer the question.Two lines are crossed by a transversal. Two angles are named. Given: m∠1=115°, m∠2=65°Prove: m∥nMatch the reason for each statement in order to complete the proof. The statements are listed in order. A reason may be used once, more than once, or not at all.(2 points)Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.m∠1=115°, m∠2=65°115°+65°=180°m∠1+m∠2=180°∠1 and ∠2 are supplementary.m∥n

Answer 1

To complete the proof that lines m and n are parallel (m∥n), we will match the statements with the appropriate reasons in order.

Here’s how the proof can be constructed:

1. Statement: m∠1 = 115°, m∠2 = 65°
   Reason: Given.

2. Statement: m∠1 + m∠2 = 180°
   Reason: Angle Addition Postulate (since we are adding the measures of angles 1 and 2).

3. Statement: 115° + 65° = 180°
   Reason: Arithmetic (Sum of the measures of angles 1 and 2).

4. Statement: ∠1 and ∠2 are supplementary.
   Reason: Definition of supplementary angles (two angles that add up to 180°).

5. Statement: m∥n.
   Reason: If two angles are supplementary and formed by a transversal, then the lines are parallel (Converse of the Same Side Interior Angles Theorem).

So the completed proof would look like this:

1. m∠1 = 115°, m∠2 = 65° – Given.
2. m∠1 + m∠2 = 180° – Angle Addition Postulate.
3. 115° + 65° = 180° – Arithmetic.
4. ∠1 and ∠2 are supplementary – Definition of supplementary angles.
5. m∥n – If two angles are supplementary and formed by a transversal, then the lines are parallel.

Feel free to ask if you need further clarification or assistance!